Every blog post that took off on Hacker News, ranked by the votes of its best submission. 2,393 posts.
Let’s say you are trying to find the distance between two points in 2D, but that these points are in a universe that “wraps around” like old video games – leaving the screen…
Whenever a student wonders why linear algebra, matrices, and vectors are important, the response from teachers usually sounds like this:
A leftover glow unlike any other — of neutrinos — has finally been seen.
Humans don’t start their thinking from scratch every second. As you read this essay, you understand each word based on your understanding of previous words. You don’t throw everything away and start thinking from scratch again. Your thoughts have persistence.
In a previous article , I already introduced manifolds and their, ahem, manifold ways. Among the many interesting comments I received about this article, some were dealing with a basic question, namely how to measure the properties of a manifold. In this article, I want to present a few concepts from Morse theory …
No reckoning allowed save the marvelous arithmetics of distance (from Smelling the Wind by Audre Lorde) Suppose a child comes up to you and says “I know 1 is odd and 2 is even, but I think 4 is mor…
Mathematical mistake/error-rates limit our understanding of rare risks and ability to defend against them.
An explanation of Variance, Covariance and Correlation in rigorous yet clear terms providing a more general and intuitive look at these essential concepts.
As of this writing, Vinay Deolalikar still hasn’t retracted his P≠NP claim, but a clear consensus has emerged that the proof, as it stands, is fatally flawed. The first reason is that weR…
In preparation for my upcoming course on random matrices, I am briefly reviewing some relevant foundational aspects of probability theory, as well as setting up basic probabilistic notation that we…
Introduction A Markov Chain is a set of transitions from one state to the next; Such that the transition from the current state to the next depends only on the current state, the previous and future states do not effect the probability of the transition. A transitions independence from future and past sates is called…
Greedy algorithms are among the simplest and most intuitive algorithms known to humans. Their name essentially gives their description: do the thing that looks best right now, and repeat until nothing looks good anymore or you’re forced to stop. Some of the best situations in computer science are also when greedy…
I wrote Planjure to learn ClojureScript and Om. It’s a fun little program. You paint islands on a canvas and run path-planning algorithms to find the optimal path for your ship to traverse from start to finish. Sailing across blue ocean is faster than hiking through green islands. The three algorithms implemented are…
With this year’s International Conference on Machine Learning (ICML) being over, it is time to have another instalment of this series. Similar to last year’s post , I shall cover several papers that caught my attention because of their use of topological concepts—however, unlike last year, I shall not restrict the…
Quarto Academic Website Template adapted by Dr. Gang He
Where do you stand in order to minimize the expected distance to walk to catch the first elevator that arrives? Maybe not where you think.
Patrick Honner tweeted a few days ago: My 7 yo pointed out that our 300 piece puzzle actually contains 18 x 18 = 324 pieces and I just don’t know what to believe anymore. — Patrick Honner (@M…
“What we call Man's power over Nature turns out to be a power exercised by some men over other men with Nature as its instrument.”
A few days ago was the anniversary of the beginning of the Cost of Knowledge boycott of Elsevier. It seems a good moment to take stock of what the boycott has achieved and to think about what progr…
Why does lining up two scales of a slide rule let you multiply numbers?
Chris Grossack's math blog and professional website.
I discuss various models of biased bit sequences, and how to extract uniform random (or close to it) output bit sequences from them, illustrated with Python code.
Simulated annealing is a method for finding a good (not necessarily perfect) solution to an optimization problem. If you're in a situation where you want to maximize or minimize something, your problem can likely be tackled with simulated annealing.
Lately, I’ve been playing around with inventing a visual writing system for lambda calculus.
Can anyone solve 1000 Opus Magnum puzzles in 24 hours? What about with assistance from bots? Will the solutions be any good? Let's find out!
My colleagues and I are disagreeing on the differentiation between machine learning and Bayesian statistical approaches. I find them philosophically distinct, but there are some in our group who would like to lump them together as both examples of machine learning. I have been favoring a definition for Bayesian…
At last, the Hamiltonian circuit problem for Rubik's Cube has a solution! To be a little more mathematically precise, a Hamiltonian circuit of the quarter-turn metric Cayley graph for the Rubik's Cube group has been found.
